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Horizontal spring, mass and nonconstant friction

  1. Apr 15, 2012 #1
    1. The problem statement, all variables and given/known data
    Hello! The problem is about spring with block attached to it. ( with spring constant = k) The system is on surface that has a friction μ increasing towards the direction of the blocks movement.

    Block is pushed -0,1m ( to the left ) from the equilubrium position and then released. The block moves from the starting position, +0,3m to the right ( +0,2m from the equilubrium position) and stops. What is the spring constant k?


    2. Relevant equations

    Spring constant = k
    Friction μ = 0,025 * x, increasing towards to the right.
    Mass of the block = 2,7 kg


    3. The attempt at a solution

    The most problematic part for me is the friction not being constant.

    I assume;

    From -0,1 m to 0,0 m the Force due to the spring and Force due to the friction are in different directions.

    From 0,0 m to 0,2 m the Force due to the spring and Force due to the friction are in same direction.

    I'm not sure, but as the accelereation ain't constant ( due to the both forces depending on some variable) should I be using some definite integrals?

    Or should I use some energy-theorem involving kinetic-energy and potential-energy?

    Sincerely yours,
    Siune

    P.S I can draw a picture about the situation and scan it here, if the explanation ain't good enough. English isn't my native language. :)
     
  2. jcsd
  3. Apr 15, 2012 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Hi Siune! :smile:
    yes, use the work energy theorem (and a bit of integration) …

    (KE + PE)initial - (KE + PE)final = work done by friction :wink:
     
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